Problem
A small business owner is applying for a small business loan and has been approved for a $50,000 loan with 4.35% annual interest. The first loan is a simple interest rate, the second loan compounds interest quarterly, and the third loan compounds interest continuously. The small business owner plans to pay off the loan in 3 years and 4 months.
• Part I: Determine the total value of the loan with the simple interest. Show all work and round your answer to the nearest hundredth.
• Part II: Determine the total value of the loan with the quarterly compounded interest. Show all work and round your answer to the nearest hundredth.
• Part III: Determine the total value of the loan with the continuously compounded interest. Show all work and round your answer to the nearest hundredth.
• Part IV: Using the values from Parts I, II, and III, explain which loan option is the best choice for the small business owner.